Humble salutations to all.
Currently there are three systems of vedanta which are considered as main and have a good following i the world. Those three are Advaita, Vishista Advaita and Dvaita. We have already seen Advaita and Vishista advaita in brief - let us now see dvaita vedanta in brief.
Dvaita vedanta was propounded and propagated by Madhvacharya (also called Ananda Teertha which is the sanyaasin name & Purna Prajna due to all-knowing nature). Madhvacharya established mathas wherein the tradition of madhvacharya is continuing to this date. Some of the famous and well-known acharyas in this school are Jaya Teertha, Vyaasa Teertha, Raghavendra....
Madhva wrote three commentaries on the Brahma Sutras. Madhva also wrote commentaries on Gita and the Upanishads. He also wrote the most famous khandana trayas (which are mayavada khandana, upaadhi khandana and prapancha mithyaatva anumaana khandana -- all works are targeted to attack the various concepts of advaita to show that advaita is faulty and wrong). Madhva is considered as the avatar of Vayu.
One of the very important feature of this school is the over-emphasis of attack on Advaita -- even though the main acharyas and real followers give emphasis to their system as well but most of the followers tend to attack advaita more than following their own system.
But it is also true that madhva and his followers have criticized advaita like anything. Vyaasa teertha's Nyaayamritam was a thorough critcisim of advaita but it was refuted and defended by Madhusudana Saraswathi in Advaita Siddhi. Most advaita acharyas hold that advaita siddhi and its commentaries have answers most of the logical issues put forth by madhva and his followers (there is a long list of refutation and counter refutation work starting from Nyaayamritam). There are different sets of acharyas like Sacchidanandendra Saraswathi and his followers who dont even bother to refute madhva as most of dvaita scholars have wrong understanding of advaita -- more of this later.
Vyaasa Teertha has written a verse which has nine basic fundamentals of dvaita -- dvaita philosophy is also called TATTVA VAADA:
SRIMAN MADHVAMATE HARI PARATARAM SATYAM JAGAT TATTVATHO
BHEDHO JEEVA GANAAH HAREH ANUCHARAAH NEECHOCCHABHAAVAGATAAH
MUKTHIRNAIJA SUKHAANOBHUTIRAMALA BHAKTHISCHA TAT SADHANAM
HI AKSHAADITRITAYAM PRAMAANAM AKHILAAMNAAYAIKA VEDHYO HARIH
1. Hari is Supreme
2. The world is real
3. There are five differences between
a. ishwara and jeeva
b. jeeva and jada
c. ishwara and jada
d. jeeva and jeeva
e. jada and jada
These differences are real
4. jeeva depends on Hari alone
5. there are three types of jeevas
a. neecha jeevas who are ever down and suffering
b. madhya jeevas who revolve around the jagat or world
c. uttama jeevas who are eligible to get liberated
6. mukthi or liberation is realizing bliss of one's nature
7. amalaa bhakthi or pure devotion is the means to realization
8. there are three pramaanas of pratyaksha or perception, anumaana or inference and sruthi or scriptures
9. HARI alone is praised and to be known through various scriptures.
Each of the above is exhaustive and vast to be dealt here.
The main emphasis of this system is broughout in a small verse of madhva thus:
etat tu paratantram sarvameva hareh sadaa
vasham ithyeva jaanaathi samsaaraat muchyathe hi sa
He who knows himself to dependent and HARI alone to be independent, he gets liberated from samsaara.
The differences between insentient entities or jadas, sentient entities or jeevas and hari is real -- ever present differences. jadas and jeevas are dependent on HARI who alone is independent. If a person knows himself to be dependent on HARI, what he does is gains devotion and surrender to HARI. Thus he gets liberated from samsaara by the grace of HARI. Liberation is not merging into the Lord but it is enjoying the bliss in oneself by getting clear knowledge about HARI & thereby the person ever lives as a devotee to HARI.
This brings us to the end of analysis of the three main systems of Vedanta. We will try to look into the other systems of vedanta in short -- but these have very few following and hence will not be of that much importance to learn or go through.
After dealing with the various systems in brief, we will again enter into the various concepts of Advaita.
Humble salutations to all.